Self-consistent Hartree theory of the role of electron-electron interactions in the electronic structure and conductance quantization of graphene nanoconstrictions

TL;DR

This paper presents self-consistent Hartree calculations of electron transport in graphene nanoconstrictions, revealing how electron-electron interactions influence conductance quantization and edge localization, with implications for experimental observations.

Contribution

It introduces a self-consistent Hartree approach to analyze electron interactions in graphene nanoconstrictions, highlighting their effects on conductance and edge states, which was not previously detailed.

Findings

Electron accumulation occurs along edges of the ribbon and certain constriction types.

Conductance quantization is more pronounced in armchair constrictions.

A prominent 2e^2/h conductance plateau emerges due to electron interactions.

Abstract

We present self-consistent calculations of electron transport in graphene nanoconstrictions within the Hartree approximation. We consider suspended armchair ribbons with V-shaped constrictions having perfect armchair or zigzag edges as well as mesoscopically smooth but atomically stepped constrictions with cosine profiles. Our calculations are based on a tight-binding model of the graphene and account for electron-electron interactions in both the constriction and the semi-infinite leads explicitly. We find that electron interactions result in (i) Electrons accumulating along edges of the uniform ribbon and along zigzag and cosine constriction edges but not along armchair constriction edges. (ii) The first subband showing almost perfect transmittance due to localization at the uniform graphene boundary except at low energies for the cases of zigzag and cosine constrictions where Bloch stop-bands form in related periodic structures. (iii) The second subband being almost perfectly blocked by the constriction. (iv) Electron interactions favor intra-subband scattering while the non-interacting electron theory predicts predominance of inter-subband scattering. (v) Conductance quantization for the first few conductance steps being more pronounced for armchair constrictions but less so for zigzag constrictions. (vi) A much more prominent 2e^2/h conductance plateau for the cosine constriction than is found in the absence of electron interactions. Possible implications for recent experiments are briefly discussed.